Problem: Simplify the following expression: ${-7(6t-7)+8(-2+t)}$
Explanation: Distribute the ${-7}$ into the first set of parentheses: $ {-7(}\gray{6t-7}{)} + 8(-2+t) $ $ {-42t+49} + 8(-2+t) $ Distribute the ${8}$ into the parentheses: $ -42t+49 + {8(}\gray{-2+t}{)} $ $ -42t+49 {-16+8t} $ Rewrite the expression to group the ${t}$ terms and numeric terms: $ {-42t + 8t} + {49 - 16}$ Combine the ${t}$ terms: $ {-34t} + {49 - 16}$ Combine the numeric terms: $ {-34t} + {33}$ The simplified expression is $-34t+33$